Asymptotic structure of symmetry-reduced general relativity

Abhay Ashtekar, Jiří Bičák, Bernd G. Schmidt

Research output: Contribution to journalArticlepeer-review

177 Scopus citations


Gravitational waves with a space-translation Killing field are considered. Because of the symmetry, the four-dimensional Einstein vacuum equations are equivalent to the three-dimensional Einstein equations with certain matter sources. This interplay between four- and three-dimensional general relativity can be exploited effectively to analyze issues pertaining to four dimensions in terms of the three-dimensional structures. An example is provided by the asymptotic structure at null infinity: While these space-times fail to be asymptotically flat in four dimensions, they can admit a regular completion at null infinity in three dimensions. This completion is used to analyze the asymptotic symmetries, introduce the analogue of the four-dimensional Bondi energy momentum, and write down a flux formula. The analysis is also of interest from a purely three-dimensional perspective because it pertains to a diffeomorphism-invariant three-dimensional field theory with local degrees of freedom, i.e., to a midisuperspace. Furthermore, because of certain peculiarities of three dimensions, the description of null infinity has a number of features that are quite surprising because they do not arise in the Bondi-Penrose description in four dimensions.

Original languageEnglish (US)
Pages (from-to)669-686
Number of pages18
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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